Finite Group Databasebeta

← #13069831

Subgroups — #13069831

Order 1408.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623356C211yesmaximal, characteristic
2C11×#417C211yesmaximal, characteristic
3C2×#66901C211yesmaximal, characteristic
4C2×#66888C211yesmaximal, characteristic, complemented
5#10622587C211yesmaximal, characteristic, complemented
6#10622577C211yesmaximal, characteristic, complemented
7#10622193C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12#66997—21no—
13#66989—21no—
14#66988—22no—
15#66979C2211yescharacteristic
16#66977—21no—
17#66977—21no—
18C2×C4×Dic11C2211yescharacteristic
19C2×#4318C2211yescharacteristic
20C11×#103—21no—
21C11×#102—21no—
22#66901—22no—
23C11⋊#95—22no—
24#66888—22no—
25#66872—21no—
26#66871—21no—
27C11×#41—21no—
28C11×#41—21no—
29C11×#41—21no—
30C11×#41—21no—
31C2×Q8×C11D411yescharacteristic
32C2×D4×C11—21no—
33C2×D4×C11D411yescharacteristic
34C22×C4×C11—21no—
35C22×C4×C11—21no—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11—21no—
38C22×Dic11D412yes—
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22—21no—
42C2×Dic22—21no—
43C2×Dic22—21no—
44C2×Dic22—21no—
45C11×M16—21no—
46C11×M16—21no—
47C2×C8×C11—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C22⋊Dic11—22no—
51C22⋊Dic11—22no—
52C22⋊Dic11—21no—
53C4⋊Dic11D411yescharacteristic
54C4⋊Dic11D411yescharacteristic
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57C4×Dic11—21no—
58C4×Dic11—21no—
59C4×Dic11—21no—
60#4318—21no—
61#4318D412yes—
62C2×C11⋊C8—21no—
63#2038—111nomaximal, Sylow
64C23×C11—21no—
65C23×C11C2×D411yescharacteristic
66Q8×C11—21no—
67Q8×C11—21no—
68D4×C11—21no—
69D4×C11—21no—
70D4×C11—41no—
71D4×C11—41no—
72C2×C4×C11—21no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×C4×C11—42no—
76C2×C4×C11—41no—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11#4111yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C2×C4×C11#4111yescharacteristic
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—41no—
90C2×Dic11—41no—
91Dic22—41no—
92Dic22—41no—
93Dic22—41no—
94Dic22—41no—
95C8×C11—41no—
96C11⋊C8—22no—
97#536—111no—
98#428—111no—
99C2×#104—111no—
100#417D1111yescharacteristic
101C2×#101—111no—
102#391—111no—
103#339—111no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—41no—
107C22×C11—41no—
108C22×C11—41no—
109C22×C11#12011yescharacteristic
110C22×C11#12111yescharacteristic
111C22×C11#12311yescharacteristic
112C4×C11—41no—
113C4×C11—81no—
114C4×C11#12111yescharacteristic
115C4×C11#12111yescharacteristic
116C4×C11#12311yescharacteristic
117C4×C11#12411yescharacteristic
118Dic11—42no—
119Dic11—42no—
120Dic11—41no—
121Dic11—41no—
122C2×#41C2×D1111yescharacteristic
123C22×Q8—111no—
124C2×M16—111no—
125C2×M16C2×D1111yescharacteristic
126C4⋊Q8—221no—
127#124—221no—
128#123—222no—
129C22⋊Q8—221no—
130C22⋊Q8—221no—
131#117—111no—
132C2×C4⋊C4C2×D1111yescharacteristic
133C2×C42—111no—
134#107—221no—
135#106—221no—
136#104—222no—
137#103—21no—
138#102—21no—
139#101—222no—
140#95—222no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11—81no—
144C2×C11#39411yescharacteristic
145C2×C11#45411yescharacteristic
146C2×C11#45611yescharacteristic
147#41—21no—
148#41—21no—
149#41—21no—
150#41—21no—
151C2×Q8—221no—
152C2×Q8—221no—
153C2×Q8—221no—
154C2×Q8—221no—
155C2×Q8—221no—
156C2×Q8—221no—
157C2×Q8C22⋊D1111yescharacteristic
158C2×D4—21no—
159C2×D4C22⋊D1111yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—112no—
163C22×C4—221no—
164C22×C4C22×D1111yescharacteristic
165M16—21no—
166M16—21no—
167M16—112no—
168M16—221no—
169C2×C8—21no—
170C2×C8—221no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—111no—
174C4⋊C4—111no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C22⋊C4—222no—
178C22⋊C4—222no—
179C22⋊C4—221no—
180C42—221no—
181C42—221no—
182C42—221no—
183C11#203811yescharacteristic, complemented, Sylow
184C23—21no—
185C23D4×D1111yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—441no—
189Q8—441no—
190Q8—441no—
191Q8—441no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—221no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—441no—
208C2×C4—441no—
209C2×C4#433911yescharacteristic
210C2×C4#433911yescharacteristic
211C2×C4D4×D1111yescharacteristic
212C2×C4D4×D1111yescharacteristic
213C2×C4#434111yescharacteristic
214C2×C4C2×C22⋊D1111yescharacteristic
215C8—41no—
216C8—222no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#6693611yescharacteristic
223C22#6693711yescharacteristic
224C22#6699011yescharacteristic
225C4—41no—
226C4—81no—
227C4—442no—
228C4—441no—
229C4—441no—
230C4—442no—
231C4#6693711yescharacteristic
232C4#6693811yescharacteristic
233C4#6698211yescharacteristic
234C4#6699211yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1062257211yescharacteristic
239C2#1062281411yescharacteristic
240C2#1062281811yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#417C2
socleC22×C11#120
prime radicalC2×C11×#41C22
hypercenter#417D11
hypocenterC11#2038
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#66888C2semidirect
5. #10622587C2semidirect
6. #10622577C2semidirect
7. #10622193C2semidirect
183. C11#2038semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106233562
C11×#4172
C2×#669012
C2×#668882
#106225872
#106225772
#106221932
#203811